LOG-SIMILARITY FOR TURBULENT FLOWS

We critically examine a recently proposed representation for turbulent energy spectra (called here log-similarity) which is predicted both b y the multifractal model and the variational approach of the small sca le intermittency. Within this representation, spectra are homothetic i n the log-log plot, the homothety factor depending on the Taylor scale based Reynolds number R(lambda). Experimental results on energy spect ra and velocity structure functions of order 2, 3 and 6 measured in di fferent flows at several R(lambda) show that this factor is beta(R(lam bda)), a measurable exponent which characterises intermittency in the inertial range. Experimentally, beta displays the existence of a trans ition in the neighbourhood of R(lambda) congruent-to 400 and for R(lam bda) tending to infinity, beta behaves as 1/ln(R(lambda)/R).